{"id":"https://openalex.org/W4237686249","doi":"https://doi.org/10.3233/fi-2021-2044","title":"On the Length of Shortest Strings Accepted by Two-way Finite Automata","display_name":"On the Length of Shortest Strings Accepted by Two-way Finite Automata","publication_year":2021,"publication_date":"2021-06-30","ids":{"openalex":"https://openalex.org/W4237686249","doi":"https://doi.org/10.3233/fi-2021-2044"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2021-2044","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2021-2044","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048233511","display_name":"Egor Dobronravov","orcid":null},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Egor Dobronravov","raw_affiliation_strings":["Department of Mathematics and Computer Science, St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia. yegordobronravov@mail.ru, dobronravov1999@mail.ru, alexander.okhotin@spbu.ru"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia. yegordobronravov@mail.ru, dobronravov1999@mail.ru, alexander.okhotin@spbu.ru","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062829009","display_name":"Nikita Dobronravov","orcid":null},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Nikita Dobronravov","raw_affiliation_strings":["Department of Mathematics and Computer Science, St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia. yegordobronravov@mail.ru, dobronravov1999@mail.ru, alexander.okhotin@spbu.ru"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia. yegordobronravov@mail.ru, dobronravov1999@mail.ru, alexander.okhotin@spbu.ru","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005683089","display_name":"Alexander Okhotin","orcid":"https://orcid.org/0000-0002-1615-2725"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexander Okhotin","raw_affiliation_strings":["Department of Mathematics and Computer Science, St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia. yegordobronravov@mail.ru, dobronravov1999@mail.ru, alexander.okhotin@spbu.ru"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg 199034, Russia. yegordobronravov@mail.ru, dobronravov1999@mail.ru, alexander.okhotin@spbu.ru","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048233511"],"corresponding_institution_ids":["https://openalex.org/I172901346"],"apc_list":null,"apc_paid":null,"fwci":0.5791,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72834792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"180","issue":"4","first_page":"315","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.7488863468170166},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.7100062370300293},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7062827944755554},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.658011794090271},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6545357704162598},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6012375950813293},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5419853329658508},{"id":"https://openalex.org/keywords/deterministic-automaton","display_name":"Deterministic automaton","score":0.5387564301490784},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.5349786281585693},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.4628870189189911},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.436676949262619},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4320683181285858},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.41811418533325195},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.2543313503265381},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18230310082435608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14270350337028503},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.06903469562530518}],"concepts":[{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.7488863468170166},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.7100062370300293},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7062827944755554},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.658011794090271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6545357704162598},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6012375950813293},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5419853329658508},{"id":"https://openalex.org/C194525867","wikidata":"https://www.wikidata.org/wiki/Q5265707","display_name":"Deterministic automaton","level":3,"score":0.5387564301490784},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.5349786281585693},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.4628870189189911},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.436676949262619},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4320683181285858},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.41811418533325195},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.2543313503265381},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18230310082435608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14270350337028503},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.06903469562530518},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2021-2044","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2021-2044","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2772918710","https://openalex.org/W2136740376","https://openalex.org/W2037872771","https://openalex.org/W185868636","https://openalex.org/W1968608348","https://openalex.org/W2488819432","https://openalex.org/W4246705858","https://openalex.org/W1987608226","https://openalex.org/W2462239665","https://openalex.org/W2966364601"],"abstract_inverted_index":{"Given":[0],"a":[1,6,76],"two-way":[2,42],"finite":[3,43],"automaton":[4],"recognizing":[5],"non-empty":[7],"language,":[8],"consider":[9],"the":[10,13,27,60,84,87],"length":[11,85],"of":[12,29,67,79,86],"shortest":[14,88],"string":[15,89],"it":[16],"accepts,":[17],"and,":[18],"for":[19,40,71,75],"each":[20],"n":[21],"\u2265":[22,82],"1,":[23,83],"let":[24],"f(n)":[25],"be":[26],"maximum":[28],"these":[30],"lengths":[31],"over":[32,64],"all":[33],"n-state":[34,41],"automata.":[35],"It":[36],"is":[37,51,90],"proved":[38],"that":[39],"automata,":[44],"whether":[45],"deterministic":[46,72],"or":[47],"nondeterministic,":[48],"this":[49],"number":[50],"at":[52,91],"least":[53,92],"\u03a9(10n/5)":[54],"and":[55,74],"less":[56],"than":[57],"(2nn+1),":[58],"with":[59],"lower":[61],"bound":[62],"reached":[63],"an":[65],"alphabet":[66,78],"size":[68,80],"\u0398(n).":[69],"Furthermore,":[70],"automata":[73],"fixed":[77],"m":[81],"e(1+o(1))mn(log":[93],"n\u2212":[94],"log":[95],"m).":[96]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}